Abstract

This paper proposes a general framework, based on weighting schemes, within which the Bayes method applied to on-line Boolean prediction can be studied. By applying standard tools in Bayes theory we propose an improved variant of the Weighted Majority algorithm for deterministic prediction. The mistake bound of our variant is asymptotically equal to the mistake bound of Weighted Majority when the latter has additional side information to optimally tune its update factor. We also show general bounds on the number of prediction mistakes made by conservative versions of Bayesian algorithms. Specific instances of our bounds match bounds previously shown for different on-line prediction algorithms proposed in the past. Finally, we study a generalization of these methods to randomized predictions.

Citations